Area between two polar curves?
Find the area inside the circle r = 3*a*cosx and outside the cardiod r = a*cosx + a, where a > 0

So always start with a diagram: I'll let you draw that. It's not too bad.
Call the first function r1. That is r1 = 3a.cos(theta) , and I assume by the way you meant to write theta, not x? And the second function r2.
Then the area is the integral
\[ \int_0^{2\pi} \int_{r_2}^{r_1} r \ dr \ d\theta \]